Let x be the first integer, then
:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
:
6x + 15 = 519
:
6x = 504
:
x = 84
:
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Our sequence is
:
84, 85, 86, 87, 88, 89
:
The third integer is 86
Answer:
The value now = $207,360
Step-by-step explanation:
Rate of increase = 20% per year = 20/100 = 0.2 per year
value 3 years ago = $120,000
interest at year 1:
20% of 120,000
= 0.2 × 120,000 = 24,000
Value at the end of year 1
= initial value + interest
= 120,000 + 24,000 = $144,000
In year 2:
20% of 144,000
= 0.2 × 144,000 = 28,800
Value at the end of year 2:
144,000 + 28,800 = $172,800
In year 3
0.2 × 172,800 = 34,560
Value at the end of year 3:
34,560 + 172,800 = $207,360
<span>[2(3+5)-2(4+1)]5
=</span><span>[2(8)-2(5)]5
=</span><span>[16-10]5
=6*5
=30</span>
Step-by-step explanation:
For every increase in the x-value by 1,
the y-value decreases by -2.
(From 3 to 1 and from 1 to -1)
Hence, slope of line k
= Rise/Run = (-2)/1 = -2. (A)
A right triangle has one leg with unknown length, the other leg with length of 5 m, and the hypotenuse with length 13 times sqrt 5 m.
We can use the Pythagorean formula to find the other leg of the right triangle.
a²+b²=c²
Where a and b are the legs of the triangle and c is the hypotenuse.
According to the given problem,
one leg: a= 5m and hypotenuse: c=13√5 m.
So, we can plug in these values in the above equation to get the value of unknown side:b. Hence,
5²+b²=(13√5)²
25 + b² = 13²*(√5)²
25 + b² = 169* 5
25+ b² = 845
25 + b² - 25 = 845 - 25
b² = 820
b =√ 820
b = √(4*205)
b = √4 *√205
b = 2√205
b= 2* 14.32
b = 28.64
So, b= 28.6 (Rounded to one decimal place)
Hence, the exact length of the unknown leg is 2√205m or 28.6 m (approximately).
